Gas pipeline networks have tremendous economic importance. As of September 2016, there were more than 2,700,000 km of natural gas pipelines and more than 4,500 km of hydrogen pipelines worldwide. In the United States in 2015, natural gas delivered by pipeline networks accounted for 29% of total primary energy consumption in the country. Due to the great importance of gas pipelines worldwide, there have been attempts to develop methods for calculating network flow solutions for gas pipeline networks. Some solutions involve formulating the problem as a nonconvex, nonlinear program. However, such methods cannot effectively scale for large gas pipeline networks. Other approaches involve stipulating in advance the direction of the flow in each pipeline segment. This approach has the advantage of reducing the complexity of the optimization problem.
However, not allowing for flow reversals severely restricts the practical application. Still other approaches formulate the solution as a mixed-integer linear program. However, constructing efficient mixed-integer linear program formulations is a significant task as certain attributes can significantly reduce the solver effectiveness.